That all recently changed with a new free ferry service that leaves from Fulton Ferry landing on weekends. Head on over to the Gov. Island website for schedule information and event listings for the island. Make sure to check the site before you go though, because the ferry doesn't always run.
In related news, the folks over at Added Value/The Red Hook Community Farm have recently opened a second farm at Governor's Island! Crops should be ready for sale sometime in late July, and proceeds will go towards providing stipends to local youth that work at the Red Hook farm, reports the NYTimes.
Image from NYTimes